The testing centre in the car park of Maltby Leisure Centre, had to close early on Tuesday (April 6) after stones were thrown at staff, according to police.
South Yorkshire police's Rotherham South Neighbourhood Policing Team said "local youths" were believed to have been "throwing stones at the site and staff".
Alexander Stafford Rother Valley's MP called the behaviour "unacceptable", and called for a "zero tolerance approach".
Mr Stafford said: "If you know who is involved, do report them to the police.
“The only way we can defeat Covid is by vaccinating and testing. If our local testing site is forced to close then it makes it harder to defeat the virus."
A spokesperson for Rotherham Council said they are "disappointed" at the incident, and that measures to ensure staff's safety are being put in place.